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3 years ago

35 Points!

Mathematics

1 answer:

a_sh-v [17]3 years ago

4 0

Answer:

The expressions are not equivalent.

Step-by-step explanation:

Three-tenths of the total volume, v = $\frac{3}{10} (v)$

= 0.3 × v --- (1)

But, 310x is 310 × v --- (2)

Since (1) and (2) represent the same volume,

0.3 × v = 310 × v

Divide both sides by v,

0.3 = 310 which is a contradiction.

Therefore, the expressions are not equivalent.

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Solve the inequality for x 3^(6x+18)<27^(3x)

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Answer:

$\displaystyle x > 6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients
Factoring

Algebra II

Exponential Rule [Powering]: $\displaystyle (b^m)^n = b^{m \cdot n}$
Solving exponential equations

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle 3^{6x + 18} < 27^{3x}$

Step 2: Solve for x

Rewrite: $\displaystyle 3^{6x + 18} < 3^{3(3x)}$
Set: $\displaystyle 6x + 18 < 3(3x)$
Factor: $\displaystyle 3(2x + 6) < 3(3x)$
[Division Property of Equality] Divide 3 on both sides: $\displaystyle 2x + 6 < 3x$
[Subtraction Property of Equality] Subtract 3x on both sides: $\displaystyle -x + 6 < 0$
[Subtraction Property of Equality] Subtract 6 on both sides: $\displaystyle -x < -6$
[Division Property of Equality] Divide -1 on both sides: $\displaystyle x > 6$